After finishing a chapter on Rank-Nullity in linear algebra I came across the following problem:
Suppose that $M,N$, are subspaces of a finite-dimensional vector space $V$ such that the dimensions of
$(M+N)/N = 2$,
$(M+N)/M = 3$,
$(M \cap N) = 4$
Then what are the dimensions of $N$, $M$, and $M+N$.
$\dim (M+N)/N = \dim (M+N) - \dim (N) = 2$, and
$\dim (M+N)/M = \dim (M+N) - \dim (M) = 3$, Thus $\dim (N) - \dim(M) = 1 $ . This is where I am stuck. Hints appreciated.